Mathematicians and the Market by hcj


									Geoff Davis
                                                                                            Mathematics Department
                                                                                            Dartmouth College
                                                                                            Hanover, NH 03755
                                                                                            (603) 646-1618 phone
Preprint, Notices of the AMS, Nov. 1997                                                     (603) 646-1672 fax

Mathematicians and the Market

            Young mathematicians have been facing dismal job prospects throughout the nineties.
            The fall unemployment rate for new Ph.D.s in the U.S., as measured by the AMS-IMS-
            MAA Annual Survey (Second Report), rose from 2.5% in 1990 to a peak of 13.2% in
            1994 . Unemployment rates have fallen moderately since to the current level of 9.5% in
            1996. This is not the first time that labor market problems have plagued mathematics.
            The early seventies saw a similar situation. The Ph.D. glut of the seventies had far-
            reaching consequences. It led to drastic cutbacks in funding for graduate education from
            which it took nearly 15 years to recover. The effects of the present labor market woes are
            already visible and dramatic, and they will certainly be damaging to mathematics in the
            long term. As I document below, the high unemployment rates facing recent Ph.D.s are
            only the tip of the iceberg.

            A variety of external factors have contributed to the present situation. Changes in funding
                       Ph.D. Production legislation, and the finances of higher education
            levels, recent immigration and U.S. Unemployment, Annual Survey, 2nd Report have all played
            a role in the present problems faced by Ph.D.s. It is all too easy to blame outside forces
               14%                                                                          1250
            beyond our control for our troubles, however. The truth is that we in the mathematics
            community share the responsibility for the current employment crisis. Our community has
            U.S. Unemployment

            dramatically expanded production of Ph.D.s without questioning whether there was

                                                                                                                     New Ph.D.s
            sufficient demand for our product. Even after five years of serious and1050
                8%                                                                            sustained
            employment problems, we have done little to adapt to the changes in the 950
                6%                                                                          market for
              Our community has failed to provide answers to the problems facing recent graduates.
                 0%                                                                                     750
                                               years 85 86 87 88 89 90                     ask 94 95 96
              What is more,80after five 83 84 we have barely begun91to 92 93the right questions in a
                      78   79       81   82
              systematic way. What are the effects of the current labor market problems on the
                                                U.S. Unemployment Rate Number of New Ph.D.s
              mathematics community as a whole? What forces have contributed to these problems?
              What are effective remedies? I address AMS-IMS-MAA Annual Survey, below, providing partial
         ? Figure 1 Ph.D. production and fall U.S. unemployment, each of these questions Second Report
              answers when data exists, and pointing out the key gaps in our current understanding. I
              conclude by describing some specific steps that the mathematical societies can take to
              improve the current labor market situation for mathematics Ph.D.s.

 How have employment problems affected the mathematics
 community as a whole?

            The high unemployment rate for new Ph.D.s in the fall after graduation is a familiar fact in
            our community. However, the current labor market problems have had pernicious effects
              The unemployment rate reported in the Notices is biased downward because it excludes unemployed Ph.D.s
            outside the U.S. The U.S. unemployment rate reported here is computed by dividing the number of Ph.D.s in the
            U.S. still seeking employment in the fall by the total number of Ph.D.s known to be in the U.S. All numbers come
            from the Annual Report, Second Report, unless otherwise noted.
  Markets for Mathematicians, Geoffrey M. Davis,

           on all levels of mathematics, and these are considerably less well known. I first examine
           these effects to show just how damaging the labor market problems have been.

Unemployment and Underemployment

           Consider the unemployment information presented in the AMS-MAA-IMS Annual Survey.
           The 8.1% reported unemployment rate for 1996 is an important measurement, but it hides
           as much as it reveals. First of all, the Annual Survey figures systematically underestimate
           total unemployment rates by not taking into account unemployment among doctorates
           outside the U.S. The 8.1% figure is the ratio of unemployed doctorates known to be in the
           U.S. to the total number of doctorates whose whereabouts are known. If we compute
           instead the ratio of unemployed doctorates in the U.S. to the total number of doctorates
           known to be in the U.S., we obtain a more relevant U.S. unemployment rate of 9.5%.

           The reported unemployment rate is distorted by a second factor as well. Some
           departments provide a form of welfare for Ph.D.s, offering temporary positions to
           graduates who are unable to find work elsewhere. It is not known how widespread this
           practice is, but the fact that nearly one quarter of Ph.D.s hired by U.S. doctoral degree-
           granting programs in 1996 (6.5% of all Ph.D.s known to be in the U.S.) were hired by the
           departments that granted them their degrees is telling. Furthermore, 3.8% of the
           employed Ph.D.s were working part-time, with at least 20% of these part-time employees
           still looking for full-time work. Even in the improved conditions of 1996, on the order of 16%
           of Ph.D.s in the U.S. were either unemployed, working less than they would like, or
           working for the same institution that granted them their degree.

           The decrease in the U.S. unemployment rate from 12.8% in 1995 to 9.5% in 1996 is
           certainly encouraging. However, the simplest explanation for the fact that 38 fewer Ph.D.s
           were still looking for work in the U.S. in the fall of 1996 than in 1995 is that there were 73
           fewer Ph.D.s granted in 1996 than 1995.

           Little is known about what happens to Ph.D.s beyond the first year after obtaining their
           degrees. The AMS conducted a study of the employment status of the class of 1991 two
           years after they obtained their degrees. In the fall after their graduation, 6.1% of the 1991
           Ph.D.s in the U.S. were unemployed. Those who obtained short-term positions had a
           much harder time during their second round of job seeking. Of the 1991 Ph.D.s employed
           in U.S. academic institutions who changed jobs, 20% were unemployed in the fall of 1993.
           There has been no follow-up on this disturbing finding.

Erosion of Opportunities

           175 years ago economist David Ricardo observed, “labor is dear when it is scarce and
           cheap when it is plentiful.” Not surprisingly, an 8% decline in real 9-month teaching and
           research salaries for new Ph.D.s has accompanied the increase in Ph.D. supply between
           1989 and 1996. Moreover, a more subtle change is occurring. There is a hidden
           downward trend in total compensation for new Ph.D.s that is occurring as the types of jobs
           held by new Ph.D.s change. New Ph.D.s in academia are increasingly employed as
           temporary rather than tenure-track employees. Between 1990 and 1995, the number of
           full-time non-tenure-eligible faculty in traditional math departments (Groups I-III) increased
           by 37%. At the same time the number of tenure-track faculty fell by 27%. Temporary
           faculty now comprise 56% of all non-tenured faculty in traditional math departments.

Markets for Mathematicians, Geoffrey M. Davis,

         In addition to having no job security, temporary workers receive fewer benefits than tenure-
         track employees do. Furthermore, temporary employment delays entry onto the tenure-
         track salary ladder. Each year on postdoctoral-level wages delays the transition to
         assistant professor salary levels by one year, and results in one less year as a full
         professor. Thus, total lifetime earnings of new doctorates have been depressed.

                                      9-month salaries for new PhDs (in 1996 dollars)


















                Figure 2 Median nine month teaching/research salaries for new math Ph.D.s in 1996 dollars

        ? Figure 3 Faculty recruiting at Doonesbury’s fictional Walden College, Garry Trudeau, 9/9/96, 9/11/96, 9/12/96.

         An increase in the amount of time required to earn a Ph.D. represents a second form of
         reduction in lifetime earnings. National Research Council data show that the median time
                                     *                                                              4
         to degree for math Ph.D.s has increased from 6.5 to 8.0 years between 1982 and 1993.
         The current Ph.D. oversupply aggravates this problem by providing strong incentives for
         students to remain in graduate school for longer and longer periods of time in the hope that
         additional time for research will make them more marketable.

         At present, no information is available on the average amount of time that new doctorates
         spend in temporary positions. Little is known about average total compensation for
         postdoctoral researchers or the effect of temporary positions on the time to tenure. Such
         information is essential for obtaining a true measure of the health of the profession.

          The NRC measure of time to degree is the total number of years between starting graduate study and obtaining
         a Ph.D. This number includes time spent in masters programs at institutions other than the doctoral granting one
         as well as time off from graduate study.

  Markets for Mathematicians, Geoffrey M. Davis,

Declining Enrollments

           The opportunity costs of graduate school have become increasingly difficult for prospective
           students to justify as the prospects and compensation for Ph.D.s decline and the time to
           degree increases. The median salary this year for new math Ph.D.s in 9-month teaching
           and research positions, the most common type of academic position held by new Ph.D.s,
           is $36,000. This is less than the $37,500 to $41,400 starting salaries commanded by 1996
           bachelors degree recipients in electrical, computer, or chemical engineering. To our most
           talented students, the mere $6,000 difference in starting salary over that for mathematics
           bachelor’s degree holders does not make a strong economic case for years of intensive
           postbaccalaureate training amidst deteriorating employment conditions.

           There is considerable evidence that labor market considerations play a strong role in
           determining educational and career choices for young people. In the words of Ed David,
           author of the David reports, “That [mathematics education is one of the best preparations
           for almost any career] may very well be true, but the students must believe that, or we
           won't have any students. And at the moment they don't appear to believe it.” A recent
           AMS study bears this out. Applications to graduate programs in mathematics fell by 30%
           between the fall of 1994 and the fall of 1996. Moreover, the number of first year full-time
           graduate students in traditional math departments (Group I, II, and III schools) declined by
           roughly 23% between 1991 and 1996. The students we are losing are those with sufficient
           breadth of talent to pursue other opportunities. We are driving out intellectual diversity at
           precisely the time we need it most.

           An anecdote of Harvard labor economist Richard Freeman puts these trends into
           perspective. Freeman was invited to speak to the physics department at the University of
           Chicago during the height of the physics employment crisis in the seventies. He writes,

                   When I finished the presentation, the chairman shook his head, frowning deeply…. ―You’ve
                   got us all wrong,‖ the chairman said gravely. ―You don’t understand what motivates people
                   to study physics. We study for love of knowledge, not for salaries and jobs.‖ ―But…,‖ I was
                   prepared to give … arguments about market incentives operating on some people on the
                   margin, when the students – facing the worst employment prospects for graduating
                   physicists in decades – answered for me with a resounding chorus of boos and hisses.
                   Case closed.8

           What Freeman does not mention is his response to assertions such as those made by the
           chairman, something to the effect of, “Terrific. If that’s true, a 5% voluntary pay cut by
           senior scientists should be enough to prop up the market for entering physicists.” This
           may have made his point.

  Markets for Mathematicians, Geoffrey M. Davis,

Loss of Departmental Autonomy?

           University administrators are under considerable pressure to cut costs in the current
           climate of fiscal retrenchment in academia. In the past, cost-cutting mechanisms such as
           departmental downsizing, faculty wage freezes, and increased teaching loads have carried
           with them the risk of the loss of top faculty members and the inability to recruit new talent.
           Might long lines of talented, inexpensive, and job-hungry new doctorates standing ready to
           fill any available position embolden institutions to employ such measures? The recent
           actions of the Regents of the University of Minnesota regarding tenure and by the
           University of Rochester to eliminate their mathematics Ph.D. program are certainly

 What forces have contributed to the present labor market problems?

           The current job crunch for math Ph.D.s has two basic causes: a rapid increase in supply
           accompanied by a large decrease in demand. Both are important for understanding the
           present situation.

Increased Supply

           769 mathematics Ph.D.s were conferred in 1985. Ten years later, that number had grown
           to 1226, an increase of nearly 60%. The factors influencing departmental determinations
           of Ph.D. production levels have been examined in a series of faculty interviews conducted
           by William Massy of the Stanford Institute for Higher Education Research. Massy and co-
           author Charles Goldman report that

                   …faculty express concern about the labor market for Ph.D.s and will do what they can to
                   place their own students—but their concern does not lead to adjustments in doctoral student
                   intakes. Faculty tend to believe that more scientifically-trained manpower is better than
                   less, and that job opportunities will materialize somehow. In any case, the department’s
                   short-run requirements for inexpensive research and teaching labor, and the desire of
                   faculty to replicate their own skills, is of stronger relevance to admissions decisions than the
                   more abstract and distant concept of labor market balance.10

           Massy and Goldman found that the primary factors used to determine Ph.D. program size
           are the number of faculty advisors available, the number of teaching assistants needed for
           staffing classes, the amount of research money available for funding assistantships, and
           the quality of the applicant pool. The recent increase in Ph.D. production has been driven
           by increases in two of these factors: funding levels and the size of the foreign applicant

          Increased Funding for Graduate Education

           Federal support for the mathematical sciences increased by 34% in constant dollars
           between 1984 and 1989 following the release of the David Report in 1984. A substantial
           fraction of these new resources were used for funding graduate education. The David
           Report sought to reinstate funding for graduate education that was cut during the Ph.D. job
           crisis of the seventies. Ironically, in so doing, it has contributed to a repetition of the
           oversupply of Ph.D.s that led to the loss of funding in the first place.

Markets for Mathematicians, Geoffrey M. Davis,

                          Increased Immigration

                           A sizable increase in the foreign student population has also contributed to the expansion
                           of Ph.D. production. The number of Ph.D.s granted to non-citizens nearly doubled
                           between 1985 and 1995, and this increase has accounted for roughly two thirds of the
                           growth in Ph.D. production over this time period. The presence of a large foreign student
                           population in and of itself is no cause for concern. Indeed, a wide variety of international
                           educational exchange programs have been designed to build ties between the scientific
                           communities in U.S. and other countries, to promote cultural exchange, and to provide
                           valuable training to the scientific workforce of less developed countries. Foreign exchange
                           students who leave the U.S. after graduation have no impact on the U.S. labor market.
                           The relevant question here is not how many non-citizen Ph.D.s are granted but how many
                           of these students remain in the U.S. after graduation.

                           The Annual Surveys do not provide data on the post-graduation statuses of non-citizen
                           doctorates. However, we can obtain a lower bound on the number in the U.S. in the fall
                           after graduation by assuming that all new Ph.D.s known to be outside the U.S. are non-
                           citizens. Figure 4 below compares the number of non-citizen Ph.D.s granted each year to
                           the number of Ph.D.s known to be outside the U.S. in the fall after earning their degrees.
                           At least 44% of non-citizen Ph.D.s were known to be in the U.S. in the fall after graduation
                           in 1985. In contrast, the 1995 figure was 67%. Although the number of Ph.D.s granted to
                           non-citizens has increased substantially over the past decade, the total number of new
                           Ph.D.s employed outside the U.S. has remained nearly constant.

                           The influx of foreign Ph.D.s does not appear to be the sudden result of one-time political
                           events such as the breakup of the Soviet Union and the post-Tiananmen Square exodus
                           from China. On the contrary, as Figure 4 shows, the increase in the graduate non-citizen
                           population has taken place gradually since the early eighties, well before these events.
                           The Immigration Act of 1990 contains provisions, included at the behest of such
                           organizations as the Association of American Universities to counteract projected Ph.D.
                           shortages , which give university employers special privileges in hiring non-citizen faculty
                           members. This legislation may well have contributed to an increase in immigration. Our
                           community needs to better understand these trends if we are to bring Ph.D. supply levels
                           in line with demand, and we need to examine their long-term implications.

                                        Estimated after-graduation addresses of non-citizen Ph.D.s
                          The Quest for Prestige?
                           Data collected by the National Research Council show that perceived program quality, as
                           measured by NRC faculty quality ratings, is strongly linked with program size. Out of
        Number of Ph.D.s

                           seventeen objective departmental criteria measured, the study found the quantity most
                           strongly correlated with perceived faculty quality was a measure of annual Ph.D.s
                           production (r = 0.73). The correlation between faculty quality and the total number of
                           students in the program is also relatively large (r = 0.63). The precise reason for this link is
                           unknown. Perhaps a large program size, a “critical mass,” is necessary to attract high
                           quality faculty members. Having graduate students is viewed by faculty as a necessary
                           condition for research productivity (and therefore program quality), and as a result faculty
                                                         to 84 idea         decreasing enrollments within 95 own
                           express strong80resistance 83 the 85 86of 87 88 89 90 91 92 93 94 their 96
                                  78 79        81 82
                           programs. Alternatively, perhaps having high faculty quality leads to expansion through
                           increased access to grant moneynon-U.S. address U.S. addresseither case, the link between
                                                               for funding students. In
                           program size and perceived quality suggests that the drive for increased program quality
           ? Figure 4 Estimated post-graduation addresses of non-citizen Ph.D.s. All Ph.D.s known to be outside the U.S. after
             graduation are assumed to be non-citizens. (Annual Survey, Second Report)

  Markets for Mathematicians, Geoffrey M. Davis,

           may result in a system-wide tendency to expand Ph.D. production regardless of job market

Decreased Demand

          Decreased Funding for Faculty Positions

           While the supply of Ph.D.s continued to increase through the early nineties, demand fell.
           The number of positions offered in math departments declined by a third between 1989
           and 1994. Much of this decrease can be attributed to rapidly rising costs for higher
           education accompanied by cuts in government funding during that time period. Combined
           federal and state support for public higher education fell by 8.8% between 1980 and 1993.
           Federal support for private institutions fell by 4% during the same period.

           The science community tremulously follows every nuance of the annual NSF budget
           negotiations. To be sure, these negotiations are important ones: NSF funding levels
           determine the availability of research assistants, summer salaries, and the speed of our
           computers. Even more important to our community, however, is the financial health of the
           overall higher education system, yet to this central issue we pay relatively little attention.

          Faculty Demographics

           Examination of the age distributions of mathematics departments shows a demographic
           bulge due to the large cohort of mathematicians hired during the late sixties and early
           seventies. The presence of this large cohort of mathematicians in their late fifties and
           early sixties, the recent elimination of mandatory retirement, and the current reduced hiring
           of junior tenure-track faculty all suggest that mathematics departments are aging. What
           are the effects of these shifting demographics? In a recent book, Professor Andrew
           Hacker puts it bluntly: “Every full professor who refuses to retire is preventing several
           young scholars from beginning their careers.” We need to understand how departmental
           demographics are evolving and what the consequences of any changes will be.

Delayed Market Feedback

           Why have market forces not corrected the present job market problems? Market forces
           do appear to be in operation: first-year enrollments in graduate programs have fallen
           substantially since the current job market woes began. The problem is one of timing.
           There is a lengthy delay between changes in first-year enrollments and the resulting
           changes in the Ph.D. supply. This type of delayed feedback system, called a “cobweb
           supply model”, is commonly used in economics for studying markets for agricultural
           commodities. The result of the delay is oscillatory behavior in the system. When market
           conditions are good, enrollments increase. Many years later, these increased enrollments
           lead to an oversupply of Ph.D.s. The resulting poor market causes enrollments to fall,
           which leads to shortage conditions years later, and so on.

           The period of the oscillation that results from the delayed feedback system is twice the
           amount of time between the decision to attend graduate school and the completion of a
           doctorate. Estimates of the median amount of time required to obtain a doctorate in
                                                17             4
           mathematics range from 6.9 years to 8.0 years. There is an additional lag since the
           decision to attend graduate school must be made at least a year before enrollment to allow
           time for applying to schools. Hence this delayed feedback model predicts an oscillation in
           Ph.D. supply with a period of roughly 16 to 18 years. This is consistent with recent history:

  Markets for Mathematicians, Geoffrey M. Davis,

           the Ph.D. supply peaked in the early seventies, bottomed out in the mid-eighties, and
           peaked again in the early nineties.

 First steps towards solving our chronic labor market problems

Assessing Supply and Demand: A “State of the Union” Report for Mathematics

           The discussion above suggests that an important factor in the current labor market
           problems is the way the supply of doctorates is currently regulated. The mathematical
           societies do not have the power to impose production quotas. Even if they did, such
           quotas would most likely create many more problems than they would solve. An important
           step that the societies can take instead is to provide sufficient information for prospective
           students, departments, and funding agencies to make more rational decisions regarding

      1. The mathematical societies should commission an annual report that analyzes
         trends affecting the supply of and demand for Ph.D.s five to ten years into the

           If departments, students, and funding agencies are to make rational enrollment and
           funding decisions, they will need information about anticipated market conditions. The
           societies can help all three parties to make informed choices by providing an annual report
           outlining major trends affecting the supply and demand for Ph.D.s. This report should
           include a discussion of the effects of current and proposed legislation, demographic
           changes, political events abroad that affect immigration, trends in industry, and so on. The
           effort in preparing the report could be shared with scientific societies in other disciplines.

           The report should be supplemented with projections of Ph.D. supply and demand. The
           time frame of the projections should be such that prospective students will have an idea
           about market conditions at the time of their graduation. Projecting supply over such a
           limited time frame is relatively straightforward given up-to-date information on current
           enrollment levels, attrition rates, and time to degree. Given the relatively strong historical
           correlation between the supply of Ph.D.s and the unemployment rate (r = 0.82), it is likely
           that supply estimates would prove to be quite valuable in assessing future market

           Projecting demand is a much more difficult than projecting supply. The point, however, is
           not to provide a perfect forecast, but rather to provide informed estimates of the effects of
           various demand-side forces. For example, an estimate of the effects of the recently
           passed five-year, $48 billion dollar tax incentive package for higher education on the
           demand for Ph.D.s in research-intensive versus teaching-intensive institutions would be
           quite valuable in assessing the need for training in teaching skills. The societies should
           draw upon outside expertise, especially that of labor market economists, in assessing the
           market conditions that will face new doctorates.

      1(a) All analyses of supply and demand should be formulated in conjunction with a
          stringent review process to avoid potential conflicts of interest.

           The notion that the supply of and demand for scientists and mathematicians can be
           predicted at all has been called into question by an infamous NSF study that projected a
           cumulative shortfall of 675,000 scientists and engineers between 1991 and 2006.           A
           follow-up article by one of the study’s authors predicted a cumulative shortfall of 153,600

  Markets for Mathematicians, Geoffrey M. Davis,

           science and engineering Ph.D.s between 1995 and 2010. Despite strong criticism of the
           study’s methodology from experts both inside and outside the NSF, the study was broadly
           distributed to policy makers. Howard Wolpe, chairman of a 1992 congressional
           investigation into the release of the study, writes, “In 1987 the NSF adopted a plan to
           double its budget in five years. There is no doubt in my mind that this shoddy science was
           knowingly disseminated by the federal government’s premier scientific agency to further
           the attainment of this goal.” Wolpe’s subcommittee found that criticism of the study “was
           ignored and even suppressed within the Foundation…. The NSF publications office …
           prevented the study from being printed as an official NSF document for over two years
           because of questions about credibility, until the director finally forced its publication.” The
           lesson to be taken from the NSF study is not that the future is completely unforeseeable.
           Rather, it is that great care must be taken in light of the potential for serious conflicts of
           interest involved in projecting Ph.D. supply and demand.

      1(b) The mathematical societies should re-evaluate the type of information collected in
          their annual departmental surveys. They should update assessments of future
          supply and demand regularly as new data becomes available.
           In 1990 the David II Report recommended substantial expansions in mathematics Ph.D.
           production just months before the bottom fell out of the job market for new Ph.D.s. The
           report justified its recommendations using projections made by Bowen and Sosa. The
           trouble with the Bowen and Sosa projections is that although they were carefully
           constructed and well documented, they relied on data and assumptions that were out of
           date. Several assumptions about Ph.D. production rates and immigration levels used by
           Bowen and Sosa were clearly wrong by the time of the David II Report’s release. For
           example, the 1987 Ph.D. production figures used for projecting future Ph.D. supply were
           old data, reflecting enrollment decisions made some 5 to 8 years earlier. First-year
           graduate enrollment figures reveal future changes in Ph.D. supply much more quickly than
           do graduation numbers. Had Bowen and Sosa had access to such enrollment data, their
           projections for the nineties may well have been quite different.

           The lesson is that assessments of supply and demand need to be made on an ongoing
           basis, and these assessments should be revised as new information becomes available.
           Projections of future market conditions will require much more detailed data on attrition
           rates, time to tenure, departmental demographics, and the hiring of non-citizen doctorates
           than is currently collected. The societies should determine the data needs of supply and
           demand models and should adjust their data gathering accordingly. These data should be
           made public to facilitate research on the labor market for scientists.

Assessing Program Effectiveness

           The oversupply of Ph.D.s is not the only problem facing recent doctorates as they seek
           employment. A recent Board of Mathematical Sciences study of graduate programs found
           that “Many doctoral students are not prepared to meet undergraduate teaching needs,
           establish productive research careers, or apply what they have learned in business and
           industry.” Furthermore, higher education is changing rapidly as student bodies become
           more heterogeneous in terms of ethnicity, income, age, and levels of preparation. In a
           recent essay in the New York Times Magazine about these changes on campus,
           Professor Louis Menand writes,

Markets for Mathematicians, Geoffrey M. Davis,

            The academic job market is bad everywhere, but the reason often given by elite universities –
            which is that there are too many ―lesser ranked‖ doctoral programs – is disingenuous. In many
            cases, the top-ranked programs are the ones having trouble placing their graduates. The reason
            may be that their students’ training is perceived as too specialized, and their teaching experience
            as too narrow, by many of the schools where jobs are available.25

         What kinds of training programs are effective for various types of departmental missions?
         What is the best way to prepare students for careers at small liberal arts colleges? For
         careers at research universities? For careers in industry? If mathematics doctorates are to
         obtain employment of the type that they seek in the rapidly changing workplace, it is
         imperative that they receive the proper training. “My experience convinces me that
         graduate education can be changed to reflect the real needs of the profession, and the
         changes would not even have to be far-reaching. But we will have to be prepared to give
         up the idea that departments and schools have only minimum collective responsibility for
         the outcome,” writes former Stanford president Donald Kennedy.

    2. The mathematical societies should collect and make publicly available information
       on graduate placement rates for all Ph.D. programs.
         A recent National Research Council report recommends that information on graduate
         placement rates for individual programs be gathered by the research community and
         made available on the Internet. Publicly available placement data would provide an
         invaluable measure of program effectiveness in preparing students for a wide variety of

         The outcome data collected for the new ratings would make it possible for the first time to
         evaluate program characteristics based on empirical considerations. For example,
         increasing the breadth of doctoral education has been widely advocated as a method for
         improving the job prospects of Ph.D.s. However, a number of mathematicians have
         raised concerns about the tradeoff between breadth and depth. Is breadth or depth more
         important, and in what contexts? This is a question best answered by looking at data on
         outcomes. Outcome data would serve to highlight a broad range of program
         characteristics that contribute to students’ preparation for successful careers.

         Public outcome data would enable prospective students to make more informed choices
         about what graduate school to attend. They would steer students toward programs with
         graduate outcomes closely matching students’ own career aspirations. Outcome data
         would also provide students with realistic career expectations. Outcome data are but one
         factor among many for students to consider in choosing a graduate program. Other
         information that would be helpful includes data on time to degree, degree completion
         rates, and financial aid.

         A key issue in the gathering of placement data is that of how to assess graduate
         outcomes. The fact that a program’s graduates are employed does not indicate whether
         they are employed in jobs appropriate for their level of training. Who decides what is a
         positive graduate outcome? The answer is simple: we should turn to the graduates
         themselves for answers. Measures of the success of graduate outcomes should be
         based on responses of recent graduates to questions regarding their job satisfaction, the
         degree to which their training prepared them for their current positions, and the extent to
         which they use skills acquired in graduate training in their current positions. No value

  Markets for Mathematicians, Geoffrey M. Davis,

           judgment needs to be made on the relative merits of industrial versus academic
           employment except by the doctorates themselves.


           The environment in which mathematicians operate is changing rapidly. If our community
           is to govern itself in a responsible manner, it is imperative that we understand and adapt to
           these changes. Our reluctance to examine difficult issues such as the determination of
           enrollment levels, immigration, changing faculty demographics, and the effectiveness of
           various types of training programs neither makes these issues disappear nor alters their
           effects. The mathematical societies have the opportunity to take a strong leadership role
           here. Better information on the market for Ph.D.s and an assessment of the effectiveness
           of different types of training programs are not a cure-all prescription, but they do represent
           an important first step. We in the mathematics community need to take a more active role
           in solving our current labor market problems and in preventing future ones. The future of
           the profession and the next generation of mathematicians depend upon it.


           The author would like to thank Sue Minkoff, Eric Weinstein, and many others for helpful
           feedback and comments. He also thanks the Digital Signal Processing group at Rice
           University for their generous hospitality during the writing of this paper.

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Markets for Mathematicians, Geoffrey M. Davis,

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